Political_Science_135_-_Fall_2005_-_Powell_-_Final

Political_Science_135_-_Fall_2005_-_Powell_-_Final - Name:_...

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Name:_______________________ GSI:_______________________ SID:_______________________ G AME T HEORY IN THE S OCIAL S CIENCES Political Science 135/Economics 110 Final Examination Fall 2005 I NSTRUCTIONS : This final examination is open book and open note. Answer all of the following questions. There are 170 points which works out to one point per minute. Budget your time carefully. Some questions are hard and others are easy. If you are stuck on a question, come back to it. Use the blank pages if necessary, and, obviously, you should use additional paper if you need it. Be sure to show your work and justify your answers to all questions so that you may be given partial credit if you add 3 and 3 and get 7!! (Those who will be grading this are especially sympathetic to those who are arithmetically challenged.) Good luck and have a good holiday vacation.
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SID:_______________________ Question 1 (25 Points/25 minutes): Fair Divisions. Groups of people often have to decide how to divide their collective assets fairly. In particular when partnerships go out of business, the partners frequently have to divide assets that are hard to value. This question focuses on how a group can divide an asset fairly. Three players, D , 2 and 3 , have to divide a pie of size one among themselves. Each prefers more pie to less. They decide to divide the pie by letting D , the divider, cut the pie into three pieces, l, m, s where l is at least as large as m ( and m is at least as large as s () . After D cuts the pie, 2 chooses its slice and then 3 chooses its slice with D getting what is left. ) lm ms (a, 5 pts) Represent the situation above as a game in extensive form by drawing the rest of the tree. D ( l,m,s ) 2 m s l,m,s l,s,m 3 l Key: ( D 's payoff, 2 's payoff, 3 's payoff) 1
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SID:_______________________ (b, 10 pts) What is the backwards-programming equilibrium of the game and how much of the pie does each player get in equilibrium. (c, 10 pts) Suppose the group is larger. In particular, there are N players: a divider D , and 2 , 3 , …, N . D now cuts the pie into N pieces after which 2 chooses which slice it wants, then 3 chooses, then 4 chooses and so on. D gets the left over slice after everyone else has chosen. How should D cut the pie, i.e., what is D ’s backwards-programming equilibrium strategy in this N player game? Be sure to explain your answer. 2
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SID:_______________________ Question 2 (53 Points/53 minutes): Presidential Veto Threats. Following Senator John McCain, the US Congress is considering a law that would prohibit the use of “extreme measures” against anyone being held in US custody. The President has threatened to veto, and Vice President Cheney has been publicly lobbying Congress to allow an exception for the CIA. In the game below, Congress must decide how large of an exception e it will make to the President who can then sign the legislation or veto it. If the President signs, the Congress and President’s payoffs are 30 – e and e , respectively. If the President vetoes the measure, the Congress receives -10, and the President gets v .
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This note was uploaded on 04/06/2010 for the course POL SCI 135 taught by Professor Powell during the Spring '04 term at University of California, Berkeley.

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Political_Science_135_-_Fall_2005_-_Powell_-_Final - Name:_...

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